Pfaffian Formulation of Schur's $Q$-functions

Abstract

We introduce a Pfaffian formula that extends Schur's $Q$-functions $Q_{\lambda }$ to be indexed by compositions $\lambda$ with negative parts. This formula makes the Pfaffian construction more consistent with other constructions, such as the Young tableau and Vertex Operator constructions. With this construction, we develop a proof technique involving decomposing $Q_{\lambda }$ into sums indexed by partitions with removed parts. Consequently, we are able to prove several identities of Schur's $Q$-functions using only simple algebraic methods.

29 pages

References in corpus (1)

• A spin analog of the plethystic Murnaghan-Nakayama rule

Cited by in corpus (1)

• Plethysm Stability of Schur's $Q$-functions